Algebra Seminar: talk by Steffen Kionke

Charlotte Scott Centre for Algebra

On this Wednesday, the 16th of November 2022, Steffen Kionke (University of Hagen) has virtually visited the Charlotte Scott Centre for Algebra and gave us a talk. The seminar was attended by members of the University of Lincoln and of the Lund University (Sweden).

Title: Upper bounds for the first L2-Betti number of groups

Abstract: Over the last 30 years L2-Betti numbers have become a major tool in the investigation of infinite groups with intriguing applications. After a short introduction to L2-invariants, we take a closer look at the first L2-Betti number. We explain how the first L2-Betti number can be studied using the geometry of the Cayley graph and present a simple method to extract upper bounds. Some applications are discussed. For instance, the bounds can be used to prove the vanishing of the first L2-Betti number of Burnside groups of large prime exponent. A remarkable feature of the…

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